Static Equilibrium in Fluids_ Pressure and Depth

							                             Static Equilibrium in Fluids: Pressure and Depth

1. Hoover Dam is 221 m deep. What is the water pressure at the base of the dam?

2. In a hydraulic system the smaller piston has a diameter of 3.80 cm and the larger piston has a diameter of
53.0 cm. What force on the smaller piston will balance a 20.0 kN force on the large piston?



3. In the hydraulic system shown the piston on the left has a diameter of 4.5 cm and
 a mass of 1.7 kg. The piston on the right has a diameter of 12 cm and a mass of 3.2 kg.
If the density of the fluid is 750 kg/m3, what is the height difference h between the two
pistons?




4. A wooden water tower is filled with fresh water to a depth of 5.5 m. What is the pressure at a depth of
(a) 4.0 m and (b) 5.0 m? Wooden water towers have metal bands wrapped around them. (c) Why are the
bands more closely spaced near the bottom of the tower?

5. A circular wine barrel 75 cm in diameter will burst if the net upward force exerted
on the top of the barrel is 6430 N. A tube 1.0 cm in diameter extends into the barrel
 through a hole in the top, as shown. Initially, the barrel is filled to the top and the tube
 is empty above that level. What weight of water must be poured into the tube in order
 to burst the barrel?




6. A patient is to receive an intravenous injection of medication. In order to work properly, the pressure of
fluid containing the medication must be 109 kPa at the injection point. Assume the pressure inside the bag
is 1 atm. (a) If the fluid has a density of 1020 kg/m3, find the height above the patient at which the bag of
fluid must be suspended. (b) If a less dense fluid is used instead, must the height of suspension be increased
or decreased? Explain.

7. A spring (k = 3.00 x 104 N/m) is between a rigid beam and the large piston of a
hydraulic lever. An empty container with negligible mass sits on the small piston.
The small piston has an area of A1, and the large piston has an area of 18.0A1. Initially
the spring is at its rest length. How many kilograms of sand must be slowly poured
into the empty container to compress the spring 5.00 m?




8. The four U-tubes shown below have two liquids in each of them. Three of the U-tubes are in static
equilibrium. (a) Identify the U-tube that is not in equilibrium and explain why. (b) For the other three, is
the density of the dark liquid greater than, less than, or equal to the density of the light colored liquid?